Modern power systems may experience decrease in stability due to the increased integration of variable generation sources that depend on power electronics converters. A common control strategy is to incorporate synthetic inertia from wind turbines, typically using state-feedback control in a single-area power system model that assumes uniform frequency. As power systems become more interconnected, different frequency behaviors can emerge in multiple areas, casting doubt on current methods that do not consider multi-area stability. Furthermore, most single-area synthetic inertia methods ignore the limitations of communication systems in real power systems. This paper proposes a decentralized synthetic inertia control strategy for a two-area power system with wind power. This approach accounts for the actual behavior of power systems in different areas and the limitations of communication systems in real scenarios. Numerical results, derived from dynamic models using actual operating data from the Chilean Power System, demonstrate that the decentralized control performs comparably to centralized control in maintaining power system stability and optimizing frequency Nadir. However, the decentralized control has the advantage of relying solely on local variables, eliminating the need for communication links between areas during operation.